Problem: Daniel is 30 years older than Umaima. For the last two years, Daniel and Umaima have been going to the same school. Nine years ago, Daniel was 4 times older than Umaima. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Daniel and Umaima. Let Daniel's current age be $d$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $d = u + 30$ Nine years ago, Daniel was $d - 9$ years old, and Umaima was $u - 9$ years old. The information in the second sentence can be expressed in the following equation: $d - 9 = 4(u - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = d - 30$ . Substituting this into our second equation, we get the equation: $d - 9 = 4($ $(d - 30)$ $ -$ $ 9)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 9 = 4d - 156$ Solving for $d$ , we get: $3 d = 147$ $d = 49$.